This study was performed to determine preservice elementary mathematics teachers' solution performance of systems of linear equations using geometric representation, algebraic representation and transition from geometric representation to the algebraic representation and the predictive role of preservice elementary mathematics teachers'…

Recent research has boosted the inclusion of introductory group theory into secondary and undergraduate mathematics education due to manifold potentials, e.g., with regards to the promotion of students' abstract thinking. However, in addition to research on cognitive processes, learners' affective characteristics have largely remained unexplored…

Does the timing of children's formal understanding of mathematical equivalence matter for algebra readiness? A change-resistance account (McNeil & Alibali, 2005) predicts that it is beneficial for children to construct a formal understanding of mathematical equivalence in the early grades before overly narrow operational patterns become…

In this study we investigated the relationship between urban eighth grade students' Hands-On Exposure to Algebraic Thinking (HEAT) competition performance and their subsequent performance on standardized measures of mathematics achievement (ACT Composite Score, ACT Math Scores, and Louisiana Algebra End of Course Exams). It was found that the…

Fractions are highly important. Therefore, it is crucial to understand the developmental trajectory of fraction knowledge and its main predictors and consequences. Our research team has proposed that we have a neurocognitive architecture dedicated to processing nonsymbolic ratios, which serves as a startup tool for fractions: the Ratio Processing…

This study focused on how two algebraic concepts- equality and variable- predicted 8th grade students' equation solving performance. In this study, predictive design as a correlational research design was used. Randomly selected 407 eight-grade students who were from the central districts of a city in the central region of Turkey participated in…

Researchers have argued that there are strong links between primary school students' competence with fraction concepts and operations and their algebraic readiness. This study involving 162 Years 5/6 students in three primary schools examined the strength of that relationship using a test based on familiar fraction tasks and a test of algebraic…

The current study investigated college students' content knowledge and cognitive abilities as factors associated with their algebra performance, and examined how combinations of content knowledge and cognitive abilities related to their algebra performance. Specifically, the investigation examined the content knowledge factors of computational…

Proportional thinking, which requires understanding fractions, ratios, and proportions, is an area of mathematics that is cognitively challenging for many children and adolescents (Fujimura, 2001; Lamon, 2007; Lobato, Ellis, Charles, & Zbiek, 2010; National Mathematics Advisory Panel [NMAP], 2008) and "transcends topical barriers in adult…

We report on two large studies conducted in advanced algebra classrooms in the US, which evaluated the effect of replacing traditional algebra 2 curriculum with an integrated suite of dynamic interactive software, wireless networks and technology-enhanced curriculum on student learning. The first study was a cluster randomized trial and the second…

Algebra is a prerequisite for access to STEM careers and occupational success (NMAP, 2008a), yet algebra is difficult for students through high school (US DOE, 2008). Growth in children's conceptual and procedural arithmetical knowledge is reciprocal, although conceptual knowledge has more impact on procedural knowledge than the reverse…

In this paper, we examine the concept definitions a group of South African upper secondary school mathematics teachers (N = 47) express and how their understanding of the truth value, the role of variable and the syntax of expression appear in the participants' explanations for their assessment of examples and non-examples of equations. We use…

We describe the application of Hierarchical Linear Modelling (HLM) in a cluster-randomised study to examine learning algebraic concepts and procedures in an innovative, technology-rich environment in the US. HLM is applied to measure the impact of such treatment on learning and on contextual variables. We provide a detailed description of such…

Identifying the types of mathematics content knowledge that are most predictive of students' long-term learning is essential for improving both theories of mathematical development and mathematics education. To identify these types of knowledge, we examined long-term predictors of high school students' knowledge of algebra and overall mathematics…

Student transition from arithmetical understandings to algebraic reasoning is recognised as an important but complex process. An essential element of the transition is the development of a rich understanding of variables. Drawing on findings from a classroom-based study, this paper outlines the instructional tasks and pedagogical actions a teacher…